کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7378817 1480129 2016 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric
ترجمه فارسی عنوان
به سوی فیزیک بر روی فراکتال: محاسبات بردار دیفرانسیل در پیوستار سه بعدی با متریک فرکتال
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
چکیده انگلیسی
One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 444, 15 February 2016, Pages 345-359
نویسندگان
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